This is true if scores from different questions are added but not if they are multiplied. Linear scoring with multiplication is exactly the same as log scoring with addition, just easier to visualise (at least to me)
Wrong. In the 100k drop, if you know each question has odds 60:40, expected winnings are maximized if you put all on one answer each time, not 60% on one and 40% on the other.
What’s not preserved between the two ways to score is which strategy maximizes expected score.
I think the 100k drop analogy may be misleading when thinking about the final result. The final score in the version I envisage is judged on ratios between results, rather than absolute values (my explanation maybe isn’t clearly enough on this). In that case putting everything on the answer which you have 60% confidence in and being right gives a ratio of 1.67 in your favour over an honest reporting. But if you do it and get it wrong then there is an infinite ratio in favour of the honest reporting.
This is true if scores from different questions are added but not if they are multiplied. Linear scoring with multiplication is exactly the same as log scoring with addition, just easier to visualise (at least to me)
Wrong. In the 100k drop, if you know each question has odds 60:40, expected winnings are maximized if you put all on one answer each time, not 60% on one and 40% on the other.
What’s not preserved between the two ways to score is which strategy maximizes expected score.
I think the 100k drop analogy may be misleading when thinking about the final result. The final score in the version I envisage is judged on ratios between results, rather than absolute values (my explanation maybe isn’t clearly enough on this). In that case putting everything on the answer which you have 60% confidence in and being right gives a ratio of 1.67 in your favour over an honest reporting. But if you do it and get it wrong then there is an infinite ratio in favour of the honest reporting.